Solve for $x$ and $y$ using substitution. ${-x+2y = 6}$ ${x = -3y-1}$
Solution: Since $x$ has already been solved for, substitute $-3y-1$ for $x$ in the first equation. ${-}{(-3y-1)}{+ 2y = 6}$ Simplify and solve for $y$ $3y+1 + 2y = 6$ $5y+1 = 6$ $5y+1{-1} = 6{-1}$ $5y = 5$ $\dfrac{5y}{{5}} = \dfrac{5}{{5}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x = -3y-1}\thinspace$ to find $x$ ${x = -3}{(1)}{ - 1}$ $x = -3 - 1$ ${x = -4}$ You can also plug ${y = 1}$ into $\thinspace {-x+2y = 6}\thinspace$ and get the same answer for $x$ : ${-x + 2}{(1)}{= 6}$ ${x = -4}$